A transaction in which the buyers and sellers of a product act independently and have no relationship to each other. The concept of an arm's length transaction is to ensure that both parties in the deal are acting in their own self interest and are not subject to any pressure or duress from the other party.
Investopedia explains Arm's Length Transaction
The concept of an arm's length transaction commonly comes into play in the real estate market. When determining the fair market value of a piece of property, the price for the property must be obtained through a potential buyer and seller operating through an arm's length transaction, otherwise, the agreed-upon price will likely differ from the actual fair market value of the property.
For example, if two strangers are involved in the sale and purchase of a house, it is likely that the final agreed-upon price will be close to market value (assuming that both parties have equal bargaining power and equal information about the situation). This is because the seller would want a price that is as high as possible and the buyer would want a price that is as low as possible.
This contrasts with a situation in which the two parties are not strangers. For example, it is unlikely that the same transaction involving a father and his son would yield the same result, because the father may choose to give his son a discount.